I very much like wild boar -- for example, sausage and bacon -- very good flavor profile, tastes, etc. Not to over-complicate this, however, I also like the idea of thinking out of the box when it comes to menu item selection, yes, without alienating or offending your core clientele.
So, that said -- I think a BLT with the wild boar bacon can work well. Maybe trying a variety of other elements -- a fruit jam/spread or something. Something that can balance with the wild boar, something other than the "typical" BLT, mayo, etc. What about a taco dish utilizing the wild boar? I am not sure where you are located, but I'll guess Cape Cod, LOL. How about something with a Tex-Mex, Southwest, etc., type of flair -- instead of a pork-base, make it a wild boar based taco. There's a lot you can do with the salsa element as well -- maybe mango, jicama, avocado, etc. What about a "breakfast taco" utilizing the wild boar bacon? For lunch, do you do any pasta? While you referred to short order fare, you also said slightly upscale breakfast and lunch. Perhaps this is an opportunity to grow and expand the menu selection -- how about a special -- a pasta with a wild boar ragout. How about incorporating the bacon right into a pasta dish?
Please let us know what you ended up doing -- and good luck.